Magnon pair emission from a relativistic domain wall in antiferromagnets

Magnon emission and excitation by a relativistic domain wall at a constant velocity in antiferromagnets is theoretically studied. A pair emission due to a quadratic magnon coupling is shown to be dominant. The emission corresponds in the comoving frame to a vacuum polarization induced by a zero-energy instability of the Lorentzboosted anomalous response function. The emission rate is sensitive to the magnon dispersion and wall profile, and is significantly enhanced for a thin wall with velocity close to the effective light velocity. The Ohmic damping constant due to magnon excitation at low velocity is calculated.